Sampled Data Systems process information from the external analog world by sampling the value of a desired signal at a regular interval and then processing these samples using numerical methods implemented on a digital computer. These sampled data systems may be used in process control, communication systems, or any other applicable context.
The frequency with which a sampled data system samples an incoming signal determines the frequency that the sampled data system is able to discriminate. Specifically, according to Nyquist's Criteria, a receiver can only discriminate frequencies that are less than one half the sampling frequency. If the input signal contains components that have frequencies above this level, those components will show up as aliases within the sampled band range. Accordingly, it is common to use anti-aliasing filters to attenuate higher frequency components from the signal prior to sampling.
FIG. 1 shows an example receiver 10 that is configured to receive an analog input signal 12 and convert the analog signal into digital form for processing by a digital computer 14. As shown in FIG. 1, the receiver includes an anti-aliasing filter 16 and an analog to digital converter 18. According to the Nyquist Criteria, a digitally sampled signal can only detect frequencies that are less than ½ the sampling rate. Any frequencies above this level will alias, i.e. show up incorrectly as lower frequency components. Accordingly, an anti-aliasing filter 16 is generally used to filter out or attenuate higher frequency components from the input signal 12. Once the higher frequency components are removed from the input signal the analog to digital converter 18 samples the signal and generates a digital value representative of the value of the signal at the sampled point in time. The output of the analog to digital converter 18 is input to the digital computer 14 for further processing.
Implementing an anti-aliasing filter increases the complexity of the receiver, which increases the cost of the receiver. Additionally, since the anti-aliasing filter operates on the signal prior to digitization, anti-aliasing filters are generally implemented with analog components. This prevents the receiver from being implemented as a fully digital circuit and increases the size of the receiver. Accordingly, it would be desirable to provide a way to process the signals digitally to avoid requiring the receiver to utilize an anti-aliasing filter.